The functional brain connectivity based on resting-sate functional magnetic resonance imaging (fMRI) data has been widely studied. However, most of the analyzes, based on functional brain network construction, either limit themselves to descriptors from graph-theoretical measures and subgraph patterns, or fail to gain the whole picture of the large-scale functional brain network. Due to the curse of the dimensionality, the millions-dimension data of the correlation information from fMRIs can not be directly processed by the current machine learning method, even with the state-of-art deep learning architecture. Hence, a good representation that can be both informative and compressed is strongly desired. In this paper, we introduce a distributional representation that can provide information across high resolution regions to low resolution regions in a brain. It is believed that a good representation of functional brain connectivity can easily separate patients with brain disorders from normal controls. In our case, the difference between groups is visualized clearly with the distributional representation. The visualized group difference not only gives a visible explanation for existing techniques in functional brain network construction, but also provides extra clues for the informativeness of weak connections, which are neglected in traditional analysis. Moreover, we propose an approach with distributional representation mappings to validate the effectiveness of the features visualized in the distributional representation. We find that the mapped distributional representation improves the performance dramatically in distinguishing subjects with a given mental disorder from the control ones. The results suggests that the distributional representation is promising for further design of algorithms, such as clustering and classification, for brain disorders.